Staggered nonlinear spin generations in centrosymmetric altermagnets under electric current

Current-induced spin generations are of significant importance for electrically controllable magnetization. Due to symmetry constraints, linear spin generation is absent in centrosymmetric magnets and nonlinear contributions become crucial. However, nonlinear spin generations have few examples in centrosymmetric compensated magnets with opposite-spin sublattices, which hinders electric control of associated magnetization. Here, we study nonlinear spin generations in altermagnets with opposite-spin sublattices. In a square altermagnetic model, both staggered and uniform nonlinear spin generations appear at opposite-spin sublattices. They vary as the magnetization direction rotates, with emerging out-of-plane components that can be utilized in perpendicular magnetization switching of high-density storage devices. By first-principles calculations, out-of-plane, staggered nonlinear spin generations are found to be considerable in a typical altermagnet, Fe$_2$Se$_2$O monolayer. Our findings provide opportunities for electrically manipulating magnetization and designing energy-efficient magnetic devices based on compensated magnets.